1. What is a Perpendicular Line?

A perpendicular line is a straight line that makes a right angle (90 degrees) with another line. In coordinate geometry, two lines are perpendicular if the product of their slopes is -1.

2. How Does the Calculator Work?

The calculator uses the perpendicular line equation:

Where:

• \( m_{\perp} \) — Perpendicular slope (-1/original slope)
• \( x_0 \) — x-coordinate of the given point
• \( y_0 \) — y-coordinate of the given point

Explanation: The calculator first finds the negative reciprocal of the original slope to get the perpendicular slope, then uses point-slope form to construct the equation.

3. Importance of Perpendicular Lines

Details: Perpendicular lines are fundamental in geometry, used in constructing right angles, coordinate systems, and solving many geometric problems.

4. Using the Calculator

Tips: Enter the slope of the original line and the coordinates of a point through which the perpendicular line should pass. The calculator will provide the equation of the perpendicular line.

5. Frequently Asked Questions (FAQ)

Q1: What if the original line is horizontal?
A: The perpendicular line will be vertical with undefined slope, and the equation will be x = constant.

Q2: What if the original line is vertical?
A: The perpendicular line will be horizontal with slope 0.

Q3: Can I use this for 3D lines?
A: No, this calculator is for 2D lines only. Perpendicularity in 3D requires considering direction vectors.

Q4: How precise are the results?
A: Results are calculated with floating-point precision and rounded to 4 decimal places for display.

Q5: What if I get an error?
A: Make sure all fields are filled with valid numbers. The original slope cannot be zero if you want a defined perpendicular slope.